GLOBAL BOUND ON THE GRADIENT OF SOLUTIONS TO p-LAPLACE TYPE EQUATIONS WITH MIXED DATA  

作　　者：Minh-Phuong TRAN The-Quang TRAN Thanh-Nhan NGUYEN 

机构地区：[1]Applied Analysis Research Group,Faculty of Mathematics and Statistics,Ton Duc Thang University,Ho Chi Minh City,Vietnam [2]Nguyen Huu Huan High School,Thu Duc City,Vietnam [3]Group of Analysis and Applied Mathematics,Department of Mathematics,Ho Chi Minh City University of Education,Vietnam

出　　处：《Acta Mathematica Scientia》2024年第4期1394-1414,共21页数学物理学报（B辑英文版）

基　　金：supported by Ministry of Education and Training(Vietnam),under grant number B2023-SPS-01。

摘　　要：In this paper,the study of gradient regularity for solutions of a class of elliptic problems of p-Laplace type is offered.In particular,we prove a global result concerning Lorentz-Morrey regularity of the non-homogeneous boundary data problem:-div((s^(2)+|▽u|^(2)p-2/2)▽u)=-div(|f|^(p-2)f)+g inΩ,u=h in■Ω,with the(sub-elliptic)degeneracy condition s∈[0,1]and with mixed data f∈L^(p)(Q;R^(n)),g∈Lp/(p-1)(Ω;R^(n))for p∈(1,n).This problem naturally arises in various applications such as dynamics of non-Newtonian fluid theory,electro-rheology,radiation of heat,plastic moulding and many others.Building on the idea of level-set inequality on fractional maximal distribution functions,it enables us to carry out a global regularity result of the solution via fractional maximal operators.Due to the significance of M_(α)and its relation with Riesz potential,estimates via fractional maximal functions allow us to bound oscillations not only for solution but also its fractional derivatives of orderα.Our approach therefore has its own interest.

关 键 词：gradient estimates p-Laplace quasilinear elliptic equation fractional maximal operators Lorentz-Morrey spaces 

分 类 号：O175.25[理学—数学]